Method of Generating a Multiscale Contrast Enhanced IMage

ABSTRACT

A digital image signal is decomposed into a multi-scale representation comprising detail images and approximation images. Translation difference images are computed by subtracting an approximation image at scale s and a translated version of that approximation image. The values of the translation difference images are non-linearly modified. An amplification image is computed at least one scale as the ratio of a first image being computed by combining the modified translation difference images at the same or smaller scale and a second image created by combining unenhanced translation difference images at the same or smaller scale. Next, an enhanced multi-scale detail representation is computed by modifying at least one scale the detail image according to the amplification image at that scale. An enhanced image representation is computed by applying a reconstruction algorithm to the enhanced multi-scale detail representation. The non-linear modification of the values of the translation difference image is steered by the values of an orientation map which comprises for each pixel on a specific scale a local direction of interest.

FIELD OF THE INVENTION

The present invention relates to a method for enhancing the imagequality of an image that is represented by a digital signal.

BACKGROUND OF THE INVENTION

Commonly images represented by a digital signal such as medical imagesare subjected to image processing during or prior to displaying or hardcopy recording.

The conversion of grey value pixels into values suitable forreproduction or displaying may comprise a multi-scale image processingmethod (also called multi-resolution image processing method) by meansof which the contrast of the image is enhanced.

According to such a multi-scale image processing method an image,represented by an array of pixel values, is processed by applying thefollowing steps. First the original image is decomposed into a sequenceof detail images at multiple scales and occasionally a residual image.Next, the pixel values of the detail images are modified by applying tothese pixel values at least one conversion function. Finally, aprocessed image is computed by applying a reconstruction algorithm tothe residual image and the modified detail images.

There are limits for the behavior of the conversion functions. Greyvalue transitions in the image can be distorted to an extent that theappearance becomes unnatural if the conversion functions are excessivelynon-linear. The distortions are more pronounced in the vicinity ofsignificant grey level transitions, which may result in overshoots atstep edges and loss of homogeneity in regions of low variance facingstrong step edges. The risk of creating artifacts becomes moresignificant for CT images since they have sharper grey leveltransitions, e.g. at the interface of soft tissue and contrast media.One has to be careful using the multi-scale techniques on CT images.

A multi-scale contrast enhancement algorithm which results in a contrastenhanced image while preserving the shape of the edge transitions hasbeen described in co-pending European patent application 06 125 766.3filed Dec. 11, 2006.

In one embodiment of this method translation difference images of atleast one approximation image of the image are created at one ormultiple scales. Next, translation difference images are non is linearlymodified. Then at least one enhanced center difference image at aspecific scale is computed by combining modified translation differenceimages at that scale or at a smaller scale. Spatially-localizedphenomena derived from the image can be used to create enhanced centerdifference images.

Finally an enhanced image is computed by applying a reconstructionalgorithm to the enhanced center difference images.

This patent application also discloses another embodiment in which adigital signal is decomposed into a multi-scale representationcomprising at least two detail images representing detail at multiplescales and approximation images of which the detail images are derived.Translation difference images are computed of at least one approximationimage. Next, the translation difference images are non linearlymodified. Then an amplification image is computed at least one scale asthe ratio of 2 images wherein the first image is computed by combiningmodified translation difference images at the same or smaller scale andthe second image is created by combining unenhanced translationdifference images at the same or smaller scale. Next, an enhancedmulti-scale detail representation is computed by modifying at least onescale the detail image according to the amplification image at thatscale.

Finally an enhanced image representation is computed by applying areconstruction algorithm to the enhanced multi-scale detailrepresentation.

Generally isotropic filters are used in the decomposition andreconstruction process and an omni-directional enhancement is applied tothe coefficients in the detail images.

The isotropic design concept is justified in those cases where the imagestatistics are stationary, meaning that every patch in the image isgenerated by the same random process as every other patch of the image.However, if one looks at a region of the image where an edge or a lineor a homogeneous region might be visible, it is is clear that theunderlying process is not stationary and changes from patch to patch.

It is an object of the present invention to overcome the limitations ofthe prior art.

Such a limitation is the inability to facilitate selective detection andenhancement of image features, for example chromosome images wherein onewants to enhance chromosome bands at a particular scale and in certainorientation and position for designated DNA analysis.

SUMMARY OF THE INVENTION

The above-described aspects are realized by a method having the specificfeatures set out in claim 1. Specific features for preferred embodimentsof the invention are set out in the dependent claims.

In the context of the present invention specific terms are defined asfollows:

Multi-Scale Decomposition Mechanism:

A multi-scale (or multi-resolution) decomposition of an image is aprocess that computes detail images of the image at multiple scales of agrey value image. A multi-scale decomposition mechanism generallyinvolves filter banks for computing the detail images. Well-knowntechniques are for example: the Laplacian pyramid, the Burt pyramid, theLaplacian stack, the wavelet decomposition, QMF filter banks . . . .

Approximation Image:

An approximation image is a grey value image that represents theoriginal grey value image at the same or a larger scale, or at the sameor a lower resolution. An approximation image at a specific scale isequivalent to the original grey value image in which all is details atthat scale have been omitted (Mallat S. G., “A Theory forMultiresolution Signal Decomposition: The Wavelet Representation”, IEEETrans. On Pattern Analysis and Machine Intelligence, vol. 11, no. 7,July 1989).

Detail Image:

A detail image is defined as a pixel map that represents the differencebetween an approximation image at a certain scale and an approximationimage at a smaller scale.

Conversion Operator:

A conversion operator is an operator which generates the pixel-wisemodification of the detail pixel values as an intermediate step tocreate a contrast enhanced version of the grey value image. Such anoperator has for example been described in European patent EP 527 525.The modification is defined by a conversion function and can e.g. beimplemented as a look up table or as a multiplicative amplification.

Translation Difference Image:

The translation difference images at a scale s are a measurement ofelementary contrast in each pixel of an approximation image at scale s.They can be computed by taking the difference of the approximation imageat that scale s and a translated version. Other computations forelementary contrast are possible, e.g. the ratio of pixel with aneighboring pixel can be used in case the processing steps are precededby an exponential transform and followed by a log transform.

Center Difference Image:

A center difference image is computed by applying a combining operator(for example the summation) to translation difference images. Thecombining operator can be a linear or non-linear function ofcorresponding pixel values in the translation difference images.

Orientation Map:

The orientation map at a specific scale is a representation for eachpixel within the image of a prominent or locally dominant directiontypically associated with significant image structures.

Possible representations of orientation maps are vector maps, the polarrepresentation (angle and amplitude of the preferred direction in eachpixel), Cartesian representation (horizontal and vertical components ofthe preferred direction in each pixel). (In a more simple representationonly an angle is defined and abstraction is made of the amplitude of thedirection vectors.)

Many implementations of computing orientation maps have been describedvarying from complex mechanisms such as the n-th order gaugecoordinates, the directions of isophotes (lines in the image connectingpoints of equal intensity), to more straightforward implementations suchas the combination of the horizontal and vertical gradient image.

The orientation map can also be computed out of detail images. Anexample is the detail information generated by the edge wavelets whereinthe detail information represents the localization of edges at differentscales.

The multi-scale image processing based on the translation differenceimages that are enhanced and combined to center differences creates thepossibility to tune the enhancement to directions present in the digitalimage.

The anisotropic multi-scale image processing is based on an orientationmap as described higher that defines the preferred, local direction ofinterest for each pixel on a specific scale.

The orientation can be computed out of the approximation images, as wellas out of the detail images.

Further on two ways to implement the anisotropic multi-scale imageenhancement are described: steerable enhancement of the translationdifference images and anisotropic weighting of the is enhancedtranslation difference images. Both implementations can either beapplied independently of each other or either applied together to createenhanced center differences out of the translation difference images.

The present invention is generally implemented as a computer programproduct adapted to carry out the method of any of the claims when run ona computer and is stored on a computer readable medium.

The methods of the present invention can be applied for enhancing theimage quality of medical images such as mammographic images, imagesobtained by computed tomography etc.

Further advantages and embodiments of the present invention will becomeapparent from the following description and drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a multi-resolution image processing scheme with the centerdifference images computed out of approximation images at the samescale,

FIG. 2 is a detailed view of the advanced enhancement functional blockof FIG. 1,

FIGS. 3 and 5 illustrate different implementations of themulti-resolution image processing method according to the presentinvention,

FIG. 4 illustrates the image enhancement step of the multi-resolutionimage processing method illustrated in FIG. 3,

FIG. 6 illustrates the image enhancement step of the multi-resolutionimage processing method illustrated in FIG. 5,

FIG. 7 illustrates the computation of the enhanced center differences bymaking the enhancement of the translation differences dependent on theirorientation,

FIG. 8 illustrates the computation of the enhanced center differences bymaking their weights orientation dependent,

FIG. 9 is a legend pertaining to the symbols used in the above figures.

DETAILED DESCRIPTION OF THE INVENTION

This contrast enhancement algorithm is applicable to all multi-scaledetail representation methods from which the original image can becomputed by applying the inverse transformation.

It is applicable to the reversible multi-scale detail representationthat can be computed as a weighted sum of translation difference images.

The weighing factors and the translation offsets of the translationdifference images can be deducted from the multi-scale decomposition insuch a way that the resulting weighted sum of the translation differenceimages is either identical or an approximation of the detail pixelvalues.

For these multi-scale detail representations the contrast can beenhanced by applying the conversion operator to the center differencesbefore the weighted sum is computed.

To compute the weighted sum of translation difference images, theapproximation image at the same scale (or resolution level) or theapproximation images at the smaller scales (or finer resolution levels)can be used.

State-of-the-art multi-scale contrast enhancement algorithms decomposean image into a multi-scale representation comprising detail imagesrepresenting detail at multiple scales and a residual image.

Some of the important multi-scale decompositions are the waveletdecomposition, the Laplacian-of-Gaussians (or LoG decomposition), theDifference-of-Gaussians (or DoG) decomposition and the Burt pyramid.

The wavelet decomposition is computed by applying a cascade of high-passand low-pass filters followed by a subsampling step.

The high-pass filter extracts the detail information out of anapproximation image at a specific scale.

In the Burt pyramid decomposition the detail information is extractedout of an approximation image at scale k by subtracting the upsampledversion of the approximation image at scale k+1.

In a state of the art methods as the one disclosed in EP 527 525 acontrast enhanced version of the image is created by conversion of thepixel values in the detail images followed by multi-scalereconstruction.

All above implementations of multiscale decomposition have a commonproperty. Each pixel value in the detail images can be computed out ofan approximation image by combining the pixel values in a movingneighborhood.

In the above cases the combining function is a weighted sum.

For the wavelet decomposition the pixel values in the detail image atscale k are computed as:

d _(k+1)=↓(h _(d) *g _(k))

g _(k+1)=↓(l _(d) *g _(k))

with h_(d) a high-pass filter, l_(d) a low-pass filter, * theconvolution operator and ↓ the subsampling operator (i.e. leaving outevery second row and column).

For the wavelet reconstruction the enhanced approximation image at scalek is computed as:

h _(k) =l _(r)*(↓h _(k+1))+h _(r)*(↓f(d _(k+1)))

with h_(r) a high-pass filter, l_(r) a low-pass filter and ↑ theupsampling operator (i.e. inserting pixels with value 0 in between anytwo rows and columns).

For the Burt decomposition the pixel values in the detail image at scalek are computed as:

d _(k) =g _(k)−4g*(↑g _(k+1))

or

d _(k) =g _(k)−4g*(↑(↓(g*g _(k))))

or

d _(k)=(1−4g*(↑(↓g)))*g _(k)

with g a Gaussian low-pass filter and 1 the identity operator.

For the Burt reconstruction the enhanced approximation image at scale kis computed as:

h _(k)=4g*(↑h _(k+1))+f(d _(k))

with f(x) the conversion operator.

The Multi-Scale Detail Pixel Values as Weighted Sums

Suppose that in the Burt multi-scale decomposition a 5×5 Gaussian filteris used with coefficients w_(k,1) with k=−2, . . . 2 and l=−2, . . . ,2, the subsampling operator removes every second row and column and theupsampling operator inserts pixels with value 0 in between any two rowsand columns.

The pixel at position i,j in the approximation image g_(k+1) is computedas:

${g_{k + 1}\left( {i,j} \right)} = {\sum\limits_{s = {- 2}}^{2}\; {\sum\limits_{t = {- 2}}^{2}\; {w_{s,t}{g_{k}\left( {{{2i} + s},{{2j} + t}} \right)}}}}$

The pixel at position i,j in the upsampled image u_(k) is computed as:

${u_{k}\left( {i,j} \right)} = \left\{ \begin{matrix}{\sum\limits_{s = {- 2}}^{2}\; {\sum\limits_{t = {- 2}}^{2}\; {w_{s,t}{g_{k}\left( {{i + s},{j + t}} \right)}}}} & {{if}\mspace{14mu} i\mspace{14mu} {and}\mspace{14mu} j\mspace{14mu} {are}\mspace{14mu} {even}} \\0 & {otherwise}\end{matrix} \right.$

The pixel at position i,j in the upsampled, smoothed image gu_(k) iscomputed as:

${{gu}_{k}\left( {i,j} \right)} = \left\{ \begin{matrix}{\sum\limits_{m = {\{{{- 2},0,2}\}}}^{\;}\; {\sum\limits_{n = {\{{{- 2},0,2}\}}}^{\;}\; {w_{m,n}{\sum\limits_{s = {- 2}}^{2}\; {\sum\limits_{t = {- 2}}^{2}\; {w_{s,t}{g_{k}\begin{pmatrix}{{i + s + m},} \\{j + t + n}\end{pmatrix}}}}}}}} & {{if}\mspace{14mu} i\mspace{14mu} {and}\mspace{14mu} j\mspace{14mu} {are}\mspace{14mu} {even}} \\{\sum\limits_{m = {\{{{- 1},1}\}}}^{\;}\; {\sum\limits_{n = {\{{{- 2},0,2}\}}}^{\;}\; {w_{m,n}{\sum\limits_{s = {- 2}}^{2}\; {\sum\limits_{t = {- 2}}^{2}\; {w_{s,t}{g_{k}\begin{pmatrix}{{i + s + m},} \\{j + t + n}\end{pmatrix}}}}}}}} & {\begin{matrix}{{if}\mspace{14mu} i\mspace{14mu} {is}\mspace{14mu} {odd}} \\{{and}\mspace{14mu} j\mspace{14mu} {is}\mspace{14mu} {even}}\end{matrix}\mspace{14mu}} \\{\sum\limits_{m = {\{{{- 2},0,2}\}}}^{\;}\; {\sum\limits_{n = {\{{{- 1},1}\}}}^{\;}\; {w_{m,n}{\sum\limits_{s = {- 2}}^{2}\; {\sum\limits_{t = {- 2}}^{2}\; {w_{s,t}{g_{k}\begin{pmatrix}{{i + s + m},} \\{j + t + n}\end{pmatrix}}}}}}}} & {\begin{matrix}{{if}\mspace{14mu} i\mspace{14mu} {is}\mspace{14mu} {even}} \\{{and}\mspace{14mu} j\mspace{14mu} {is}\mspace{14mu} {odd}}\end{matrix}\mspace{14mu}} \\{\sum\limits_{m = {\{{{- 1},1}\}}}^{\;}\; {\sum\limits_{n = {\{{{- 1},1}\}}}^{\;}\; {w_{m,n}{\sum\limits_{s = {- 2}}^{2}\; {\sum\limits_{t = {- 2}}^{2}\; {w_{s,t}{g_{k}\begin{pmatrix}{{i + s + m},} \\{j + t + n}\end{pmatrix}}}}}}}} & {{if}\mspace{14mu} i\mspace{14mu} {and}\mspace{14mu} j\mspace{14mu} {are}\mspace{14mu} {odd}}\end{matrix} \right.$

to Finally, the pixel at position i,j in the detail image d_(k) iscomputed as:

${d_{k}\left( {i,j} \right)} = \left\{ \begin{matrix}{{g_{k}\left( {i,j} \right)} - {4{\sum\limits_{m = {\{{{- 2},0,2}\}}}^{\;}\; {\sum\limits_{n = {\{{{- 2},0,2}\}}}^{\;}\; {w_{m,n}{\sum\limits_{s = {- 2}}^{2}\; {\sum\limits_{t = {- 2}}^{2}\; {w_{s,t}{g_{k}\begin{pmatrix}{{i + s + m},} \\{j + t + n}\end{pmatrix}}}}}}}}}} & \begin{matrix}{{{if}\mspace{14mu} i\mspace{14mu} {and}}\mspace{14mu}} \\{j\mspace{14mu} {are}\mspace{14mu} {even}}\end{matrix} \\{{g_{k}\left( {i,j} \right)} - {4{\sum\limits_{m = {\{{{- 1},1}\}}}^{\;}\; {\sum\limits_{n = {\{{{- 2},0,2}\}}}^{\;}\; {w_{m,n}{\sum\limits_{s = {- 2}}^{2}\; {\sum\limits_{t = {- 2}}^{2}\; {w_{s,t}{g_{k}\begin{pmatrix}{{i + s + m},} \\{j + t + n}\end{pmatrix}}}}}}}}}} & {\begin{matrix}{{if}\mspace{14mu} i\mspace{14mu} {is}\mspace{14mu} {odd}} \\{{and}\mspace{14mu} j\mspace{14mu} {is}\mspace{14mu} {even}}\end{matrix}\mspace{14mu}} \\{{g_{k}\left( {i,j} \right)} - {4{\sum\limits_{m = {\{{{- 2},0,2}\}}}^{\;}\; {\sum\limits_{n = {\{{{- 1},1}\}}}^{\;}\; {w_{m,n}{\sum\limits_{s = {- 2}}^{2}\; {\sum\limits_{t = {- 2}}^{2}\; {w_{s,t}{g_{k}\begin{pmatrix}{{i + s + m},} \\{j + t + n}\end{pmatrix}}}}}}}}}} & {\begin{matrix}{{if}\mspace{14mu} i\mspace{14mu} {is}\mspace{14mu} {even}} \\{{and}\mspace{14mu} j\mspace{14mu} {is}\mspace{14mu} {odd}}\end{matrix}\mspace{14mu}} \\{{g_{k}\left( {i,j} \right)} - {4{\sum\limits_{m = {\{{{- 1},1}\}}}^{\;}\; {\sum\limits_{n = {\{{{- 1},1}\}}}^{\;}\; {w_{m,n}{\sum\limits_{s = {- 2}}^{2}\; {\sum\limits_{t = {- 2}}^{2}\; {w_{s,t}{g_{k}\begin{pmatrix}{{i + s + m},} \\{j + t + n}\end{pmatrix}}}}}}}}}} & \begin{matrix}{{{if}\mspace{14mu} i\mspace{14mu} {and}}\mspace{14mu}} \\{j\mspace{14mu} {are}\mspace{14mu} {odd}}\end{matrix}\end{matrix} \right.$

Generally, the pixel at position i,j in the detail image d_(k) can becomputed as a weighted sum of pixels in the approximation image at thesame or smaller scale k, k−1, k−2, . . . :

${d_{k}\left( {i,j} \right)} = {{g_{l}\left( {{ri},{rj}} \right)} - {\sum\limits_{m}^{\;}\; {\sum\limits_{n}^{\;}\; {v_{m,n}{g_{l}\left( {{{ri} + m},{{rj} + n}} \right)}}}}}$

with lε{0, . . . , k} and r=subsampling_factor^((l-k))

Because

${\sum\limits_{m}^{\;}\; {\sum\limits_{n}^{\;}\; v_{m,n}}} = 1$

the pixel at position i,j in the detail image d_(k) can be computed as:

${d_{k}\left( {i,j} \right)} = {{g_{l}\left( {{ri},{rj}} \right)} - {\sum\limits_{m}^{\;}\; {\sum\limits_{n}^{\;}\; {v_{m,n}{g_{l}\left( {{{ri} + m},{{rj} + n}} \right)}}}}}$${d_{k}\left( {i,j} \right)} = {{\sum\limits_{m}^{\;}\; {\sum\limits_{n}^{\;}\; {v_{m,n}{g_{l}\left( {{ri},{rj}} \right)}}}} - {\sum\limits_{m}^{\;}\; {\sum\limits_{n}^{\;}\; {v_{m,n}{g_{l}\left( {{{ri} + m},{{rj} + n}} \right)}}}}}$${d_{k}\left( {i,j} \right)} = {{c_{k}\left( {i,j} \right)} = {\sum\limits_{m}^{\;}\; {\sum\limits_{n}^{\;}\; {v_{m,n}\left( {{g_{l}\left( {{ri},{rj}} \right)} - {g_{l}\left( {{{ri} + m},{{rj} + n}} \right)}} \right)}}}}$

The term g_(l)(ri,rj)−g_(l)(ri+m,rj+n) is called a translationdifference.

It expresses the difference in pixel value between a central pixel and aneighboring pixel in an approximation image. It is a measure of localcontrast.

The weighted sum of the translation differences is called a centredifference c_(k) (i,j).

The weights can be chosen such that the center difference images areidentical to the multi-scale detail images or that they are a closeapproximation of the multi-scale detail images.

In a similar way as disclosed higher, it can be proven that the detailimages in other multi-scale decomposition methods can also berepresented as a combination of translation difference images.

The Conversion Operation

In state-of-the-art methods like the one disclosed in EP 527 525contrast enhancement is obtained by applying a conversion operator f(x)to the detail image d_(k) or, equivalently:

${f\left( {d_{k}\left( {i,j} \right)} \right)} = {f\begin{pmatrix}{{g_{l}\left( {{ri},{rj}} \right)} -} \\{\sum\limits_{m}^{\;}\; {\sum\limits_{n}^{\;}\; {v_{m,n}{g_{l}\left( {{{ri} + m},{{rj} + n}} \right)}}}}\end{pmatrix}}$

An example of such a conversion operator is the sigmoid function.Another example of such conversion operator is the contrast enhancementfunction like the one disclosed in EP 525 527. The shape of theconversion operator depends on the specific requirements of theenhancement which is intended to amplify the low-value detail pixel morethan the high-value detail pixels.

The conversion step may cause deformations of the shape of the edgetransitions in the reconstructed, contrast enhanced image. The reason isthe non-linearity of the conversion function.

Generally, the following applies to non-linear functions:

f(x + y) ≠ f(x) + f(y) or${f\left( {\sum\limits_{i}^{\;}\; x_{i}} \right)} \neq {\sum\limits_{i}^{\;}{f\left( x_{i} \right)}}$

State-of-the-art algorithms first compute the pixel values in the detailimage d_(k) as weighted sums and apply the conversion step afterwards.

By rewriting the pixel values in the detail image d_(k) as a weightedsum of translation differences, it is possible to apply the conversionstep before the summation instead of afterwards.

Contrast enhancement is now obtained by applying the conversion step tothe translation differences:

${f\left( {d_{k}\left( {i,j} \right)} \right)} = {\sum\limits_{m}^{\;}\; {\sum\limits_{n}^{\;}\; {v_{m,n}{f\left( {{g_{l}\left( {{ri},{rj}} \right)} - {g_{l}\left( {{{ri} + m},{{rj} + n}} \right)}} \right)}}}}$

In this way the shape of the edge transitions is better preserved in thecontrast enhanced, reconstructed image.

If for every scale k the detail image at that scale is computed out ofthe full resolution image g₀, and enhancement is applied to the centerdifferences, then the shapes of the edge transitions are best preservedafter reconstruction.

Different implementations of the present invention are illustrated inFIGS. 1, 3 and 5. Corresponding enhancement steps are shown in FIGS. 2,4, and 6.

FIG. 1 shows how center difference images are computed out of theapproximation images at the same scale.

FIG. 2 shows a steered enhancement block making use of orientation mapsderived from approximation images at the same or a coarser scale.

Functional Blocks A_(k)

These filtering blocks can be used to enhance the approximation imagesor to compute certain characteristics out of the approximation images,typically a horizontal and vertical gradient image. Thesecharacteristics can be used to compute the orientation maps.

In a specific embodiment the approximation images are enhanced before anorientation map is computed out of it. This can for example be performedby additional smoothing of the approximation images to reduce theinfluence of noise and irrelevant small image structures on theorientation map computation.

Also other characteristics can be computed out of the approximationimages.

Orientation Map Generator M

The orientation map at a specific scale is a representation for eachpixel within the image of a prominent or locally dominant direction ofsignificant image structures.

Possible representations of orientation maps have been described higher.

Anisotropic Enhancement

The anisotropic enhancement is performed by either (1) a steeredenhancement of the translation difference images, whereby the steeringdepends on the contents of the orientation map, or (2) by an anisotropicweighing (coefficients w_(j)) of the enhanced translation differenceimages. Both implementations can either be applied independently of eachother or either applied together to create enhanced center differencesout of the translation difference images.

Steerable Enhancement of the Translation Difference Images

Each enhanced center difference is computed as a combination of enhancedtranslation differences.

A translation difference is the difference in pixel value in anapproximation image of a central pixel with a pixel in its localneighborhood.

By using the spatial orientation of these 2 pixels w.r.t. each other,one can adapt the enhancement to modify translation differences more orless in accordance to a predefined orientation of interest.

Example (see FIG. 7—different levels in the 3D image represent differentvalues):

Suppose a noisy edge is present in a region of interest within theimage.

In order to combine enhancement of the edge while at the same timereducing the impact of noise, one could enhance the translationdifferences with an orientation perpendicular to the edge orientationand attenuate the translation differences parallel to the edge.

The latter translation differences represent unwanted, noise imagestructure, while the first ones represent the local contrast over theedge. Translation differences with an orientation in between willundergo an intermediate enhancement.

is Starting from the approximation image g_(k-m) the orientation map Mis computed by combining the horizontal and vertical gradients of imageg_(k-m). To diminish the influence of the noise to the gradientcomputations, the approximation image g_(k-m) is filtered using e.g. amedian filter resulting in the filtered image A_(k)(g_(k-m)).

The vertical en horizontal first-order gradients within the image arecomputed using the kernel {1, −1} in horizontal and vertical direction.If the orientation map M represents e.g. the local direction ofsignificant image structures (or perpendicular to it), the map iscomputed as the inverse tangent function of the ratio of the verticaland the horizontal gradient:

${M\left( {i,j} \right)} = {\tan^{- 1}\left( \frac{{ver\_ grad}\left( {{A_{k}\left( {g_{k - m}\left( {i,{j - 1}} \right)} \right)},{A_{k}\left( {g_{k - m}\left( {i,{j + 1}} \right)} \right)}} \right)}{{hor\_ grad}\left( {{A_{k}\left( {g_{k - m}\left( {{i - 1},j} \right)} \right)},{A_{k}\left( {g_{k - m}\left( {{i + 1},j} \right)} \right)}} \right)} \right)}$

This orientation map M is used as steering input for the LUT operator.

The LUT operator has 2 inputs, the translation differences and theorientation map, and generates the enhanced translation differences asoutput.

An example of such a steerable LUT operator LUT(d_(k), M(i,j)) is thecombination of a conversion operator f(d_(k)) with an extra orientationdependent amplification function Amp(θ) with θ function of theorientation map M(i,j).Examples of the conversion operator f(d_(k)) are the sigmoid functionand a contrast enhancement function like the one disclosed in EP 525527. The shape of the conversion operator depends on the specificrequirements of the enhancement which is intended to amplify thelow-value translation differences more than the high-value translationdifferences.The orientation dependent amplification function returns typically amaximum amplification factor along a preferred direction, a minimum isamplification factor for the orientation perpendicular to the preferreddirection and gradually varying amplification factors for theintermediate orientations.

An example of such an orientation dependent amplification function isthe cosine function multiplied with a constant amplification factor b.As input for this function the difference can be taken between the localdirection of interest as specified by the orientation map M(i,j) and theorientation of the translation difference at position (m,n) w.r.t. thecenter pixel of interest:

Amp(θ)=b cos(θ)

with

θ=M(i,j)−angle(d _(k)(i+m,j+n) and angle(d _(k)(i+m,j+n)=tan⁻¹(n/m)

More advanced implementations of the steerable LUT operators aremulti-dimensional look-up tables.The results of the LUT operator are enhanced translation differenceswith an extra enhancement of the translation differences along thedirection as specified by M(i, j) (indicated in FIG. 7 by the height ofthe representation of the enhanced translation differences e_(m,n)).The enhanced translation differences are then combined using isotropicweights w_(m,n) to compute enhanced center difference at position i, j.Using the same weights, a second image is created by combiningunenhanced translation difference images at the same or smaller scale.Next an enhanced multi-scale detail representation is computed bymodifying at least one scale the detail image according to theamplification image at that scale.Finally an enhanced image representation is computed by applying areconstruction algorithm to the enhanced multi-scale detailrepresentation.

Anisotropic Weighting of the Enhanced Translation Difference Images

To compute the center differences out of the translation differenceimages at each position (x, y), the weighted sum is taken of thetranslation differences. In European patent application 06 125 766.3filed Dec. 11, 2006, the weights are isotropic and no preferentialdirection is defined.

By changing the weights in accordance to their spatial orientation withrespect to the central weight, one can change the importance oftranslation differences along a predefined orientation in the total sum.

Example (see FIG. 8—different levels in the 3D image represent differentvalues):

Suppose a noisy edge is present in a region of interest within theimage.

If an enhancement of this edge is wanted while reducing the noise, onecould apply relatively higher weights to the enhanced translationdifferences with an orientation perpendicular to the edge orientationand relatively lower weights to the enhanced translation differencesparallel to the edge. The latter translation differences representunwanted, noise image structure, while the first ones represent thelocal contrast over the edge. Enhanced translation differences with anorientation in between will be taken into account with intermediateweights.

The computation of the orientation map M out of an approximation imageg_(k-m) is explained in detail in the first is embodiment.

Instead of using the orientation map M as steering input for the LUToperator, the orientation map M can also be used as steering parameterto create anisotropic weights w_(m,n).In this embodiment the LUT operator depends only on the unenhancedtranslation differences, e.g. the conversion operator f(d_(k)) asspecified above.For each position i,j within the image, the isotropic weights w_(m,n)are modified w.r.t. their orientation to the local direction of interestas specified by the orientation map M(i, j).As modification operator the mechanism of an amplification function isused as explained in the first embodiment.The isotropic weights w_(m,n) are multiplied by an orientation dependentamplification function that typically returns a maximum multiplicationfactor along a preferred direction, a minimum multiplication factor forthe orientation perpendicular to the preferred direction and a graduallyvarying multiplication factors for the intermediate orientations(indicated in FIG. 8 by the height of the representation of the weightsw_(m,n)).

An example of such an orientation dependent amplification function isthe cosine function. As input for this function the difference can betaken between the local direction of interest as specified by theorientation map M(i,j) and the orientation of the weights at position(m,n) w.r.t. the center position (0,0):

Amp(θ)=cos(θ)

with

θ=M(i,j)−angle(w _(k)(m,n) and angle(w _(k)(m,n)=tan⁻¹(n/m)

Furthermore the anisotropic weights are normalized such that the sum ofthe weights equals one.

In the last step the center difference is computed by combining is theenhanced translation differences using the anisotropic weights. Thisresults in relatively higher weights for the enhanced translationdifferences oriented along the local direction of interest as specifiedby the orientation map M(i, j).

Combinations of the enhancement methods illustrated in FIGS. 7 and 8 arealso possible.

1. A computer-implemented method for enhancing the contrast of an imagethat is represented by a digital signal wherein a. said digital signalis decomposed into a multi-scale representation comprising at least twodetail images representing detail at multiple scales and approximationimages of which the detail images are derived, an approximation image ata scale representing the grey values of said image in which all detailsat that scale have been omitted, b. translation difference images arecomputed by pixel-wise subtracting the values of an approximation imageat scale s and the values of translated versions of said approximationimage, c. the values of said translation difference images arenon-linearly modified, d. an amplification image is computed at leastone scale as the ratio of 2 images wherein the first image is computedby forming a weighted sum of said modified translation difference imagesat the same or smaller scale and the second image is created by forminga weighted sum of un-enhanced translation difference images at the sameor smaller scale, said un-enhanced difference images being differentfrom said detail images, e. an enhanced multi-scale detailrepresentation is computed by modifying at at least one scale the detailimage by applying the amplification image at that scale, f. an enhancedimage representation is computed by applying a reconstruction algorithminverting the multi-scale decomposition to the enhanced multi-scaledetail representation, wherein said non-linear modification of thevalues of the translation difference image is steered by the values ofan orientation map which comprises for each pixel on a specific scale alocal direction of interest or wherein values of weights that areapplied to the images that are summed up to form said amplificationimage are steered by the values of an orientation map which comprisesfor each pixel on a scale a local direction of interest.
 2. (canceled)3. A method according to claim 1 wherein said orientation map is deducedfrom filtered approximation images.
 4. A method according to claim 1wherein a translation difference image at a specific scale is computedout of an approximation image at the same scale.
 5. A method accordingto claim 1 wherein all of said translation difference images arecomputed out of the original image.
 6. A method according to claim 1wherein a translation difference image at a scale k is computed out ofan approximation image at scale m, wherein m represents a scale betweenscale 1 and scale k−1.
 7. A method according to claim 1 wherein thecenter difference images being weighted sums of translation differenceimages are identical to the multi-scale detail images or a closeapproximation of the multi-scale detail images.
 8. A method according toclaim 1 wherein said image is a mammographic image.
 9. A methodaccording to claim 1 wherein said image is a CT image.
 10. A computerprogram product adapted to carry out a method of enhancing the contrastof an image that is represented by a digital signal when run on acomputer, the method comprising: a. said digital signal is decomposedinto a multi-scale representation comprising at least two detail imagesrepresenting detail at multiple scales and approximation images of whichthe detail images are derived, an approximation image at a scalerepresenting the grey values of said image in which all details at thatscale have been omitted, b. translation difference images are computedby pixel-wise subtracting the values of an approximation image at scales and the values of translated versions of said approximation image, c.the values of said translation difference images are non-linearlymodified, d. an amplification image is computed at least one scale asthe ratio of 2 images wherein the first image is computed by forming aweighted sum of said modified translation difference images at the sameor smaller scale and the second image is created by forming a weightedsum of un-enhanced translation difference images at the same or smallerscale, said un-enhanced difference images being different from saiddetail images, e. an enhanced multi-scale detail representation iscomputed by modifying at at least one scale the detail image by applyingthe amplification image at that scale, f. an enhanced imagerepresentation is computed by applying a reconstruction algorithminverting the multi-scale decomposition to the enhanced multi-scaledetail representation, wherein said non-linear modification of thevalues of the translation difference image is steered by the values ofan orientation map which comprises for each pixel on a specific scale alocal direction of interest or wherein values of weights that areapplied to the images that are summed up to form said amplificationimage are steered by the values of an orientation map which comprisesfor each pixel on a scale a local direction of interest.
 11. A computerreadable medium for enhancing the contrast of an image that isrepresented by a digital signal comprising computer executable programcode adapted to carry out a method comprising: g. said digital signal isdecomposed into a multi-scale representation comprising at least twodetail images representing detail at multiple scales and approximationimages of which the detail images are derived, an approximation image ata scale representing the grey values of said image in which all detailsat that scale have been omitted, h. translation difference images arecomputed by pixel-wise subtracting the values of an approximation imageat scale s and the values of translated versions of said approximationimage, i. the values of said translation difference images arenon-linearly modified, j. an amplification image is computed at leastone scale as the ratio of 2 images wherein the first image is computedby forming a weighted sum of said modified translation difference imagesat the same or smaller scale and the second image is created by forminga weighted sum of un-enhanced translation difference images at the sameor smaller scale, said un-enhanced difference images being differentfrom said detail images, k. an enhanced multi-scale detailrepresentation is computed by modifying at at least one scale the detailimage by applying the amplification image at that scale, l. an enhancedimage representation is computed by applying a reconstruction algorithminverting the multi-scale decomposition to the enhanced multi-scaledetail representation, wherein said non-linear modification of thevalues of the translation difference image is steered by the values ofan orientation map which comprises for each pixel on a specific scale alocal direction of interest or wherein values of weights that areapplied to the images that are summed up to form said amplificationimage are steered by the values of an orientation map which comprisesfor each pixel on a scale a local direction of interest.
 12. Acomputer-implemented method for enhancing the contrast of an image, themethod comprising: a. decomposing a digital signal into a multi-scalerepresentation comprising at least two detail images representing detailat multiple scales and approximation images of which the detail imagesare derived, an approximation image at a scale representing the greyvalues of said image in which all details at that scale have beenomitted, b. computing translation difference images by pixel-wisesubtracting the values of an approximation image at scale s and thevalues of translated versions of said approximation image, c. modifyingthe values of said translation difference images non-linearly, d.computing an amplification image at least one scale as the ratio of twoimages wherein the first image is computed by forming a weighted sum ofsaid modified translation difference images at the same or smaller scaleand the second image is created by forming a weighted sum of un-enhancedtranslation difference images at the same or smaller scale, saidun-enhanced difference images being different from said detail images,e. computing an enhanced multi-scale detail representation by modifyingat at least one scale the detail image by applying the amplificationimage at that scale, f. computing an enhanced image representation byapplying a reconstruction algorithm inverting the multi-scaledecomposition to the enhanced multi-scale detail representation, whereinsaid non-linear modification of the values of the translation differenceimage is steered by the values of an orientation map which comprises foreach pixel on a specific scale a local direction of interest or whereinvalues of weights that are applied to the images that are summed up toform said amplification image are steered by the values of anorientation map which comprises for each pixel on a scale a localdirection of interest.
 13. A method according to claim 12, furthercomprising deducing said orientation map from filtered approximationimages.
 14. A method according to claim 12, further comprising computinga translation difference image at a specific scale out of anapproximation image at the same scale.
 15. A method according to claim12, wherein all of said translation difference images are computed outof the original image
 16. A method according to claim 12, wherein atranslation difference image at a scale k is computed out of anapproximation image at scale m, wherein m represents a scale betweenscale 1 and scale k−1.
 17. A method according to claim 12, wherein thecenter difference images being weighted sums of translation differenceimages are identical to the multi-scale detail images or a closeapproximation of the multi-scale detail images.
 18. A method accordingto claim 12, further comprising creating said translation differenceimage from a mammographic image.
 19. A method according to claim 12,further comprising creating said translation difference image from acomputed tomography image.